{"id":94578,"date":"2017-01-12T12:30:17","date_gmt":"2017-01-12T14:30:17","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=94578"},"modified":"2026-05-28T18:34:40","modified_gmt":"2026-05-28T20:34:40","slug":"razoes-e-proporcoes","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/razoes-e-proporcoes","title":{"rendered":"Raz\u00f5es e Propor\u00e7\u00f5es"},"content":{"rendered":"<p><b>Raz\u00e3o<\/b>\u00a0\u00e9 a compara\u00e7\u00e3o matem\u00e1tica entre duas grandezas (uma divis\u00e3o), enquanto\u00a0<b>propor\u00e7\u00e3o<\/b>\u00a0\u00e9 a igualdade entre duas raz\u00f5es. Esses conceitos s\u00e3o fundamentais para resolver problemas de porcentagem, velocidade m\u00e9dia, escalas e regra de tr\u00eas.<\/p>\n<p>Uma\u00a0<b>raz\u00e3o<\/b>\u00a0compara duas ou mais quantidades, enquanto uma\u00a0<b>propor\u00e7\u00e3o<\/b>\u00a0\u00e9 uma equa\u00e7\u00e3o que afirma que duas raz\u00f5es s\u00e3o iguais. Juntas, elas s\u00e3o os conceitos matem\u00e1ticos fundamentais usados \u200b\u200bpara ajustar receitas, calcular tempos de viagem e analisar dados estat\u00edsticos.<\/p>\n<p>Na matem\u00e1tica, a raz\u00e3o estabelece uma compara\u00e7\u00e3o entre duas grandezas, sendo o coeficiente entre dois n\u00fameros.<\/p>\n<p>J\u00e1 a propor\u00e7\u00e3o \u00e9 determinada pela igualdade entre duas raz\u00f5es, ou ainda, quando duas raz\u00f5es possuem o mesmo resultado.<\/p>\n<p>Note que a raz\u00e3o est\u00e1 relacionada com a opera\u00e7\u00e3o da divis\u00e3o. Vale lembrar que duas grandezas s\u00e3o proporcionais quando formam uma propor\u00e7\u00e3o.<\/p>\n<p>Ainda que n\u00e3o tenhamos consci\u00eancia disso, utilizamos cotidianamente os conceitos de raz\u00e3o e propor\u00e7\u00e3o. Para preparar uma receita, por exemplo, utilizamos certas medidas proporcionais entre os ingredientes.<\/p>\n<p>Sendo a e b dois n\u00fameros racionais, com b \u2260 0, denomina-se raz\u00e3o entre a e b ou raz\u00e3o de a para b o quociente do primeiro pelo segundo: <img decoding=\"async\" class=\"size-full wp-image-94582 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_752-Jan.-12-12.17.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"21\" height=\"39\" \/>ou a : b.<\/p>\n<p>A raz\u00e3o <img decoding=\"async\" class=\"size-full wp-image-94582 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_752-Jan.-12-12.17.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"21\" height=\"39\" \/>\u00a0ou a : b pode ser lida de uma das seguintes maneiras:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-94583 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_753-Jan.-12-12.18.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"502\" height=\"41\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_753-Jan.-12-12.18.jpg 502w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_753-Jan.-12-12.18-300x25.jpg 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Quando escrevemos uma raz\u00e3o na forma fracion\u00e1ria ou na forma de divis\u00e3o, o primeiro n\u00famero denomina-se antecedente e o segundo n\u00famero, consequente.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-94585 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_754-Jan.-12-12.19.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"490\" height=\"131\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_754-Jan.-12-12.19.jpg 490w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_754-Jan.-12-12.19-300x80.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<p>Exemplos:<\/p>\n<p>1) A raz\u00e3o entre 8 e 6 \u00e9 <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-94587 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_755-Jan.-12-12.21.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"45\" height=\"52\" \/>\u00a0= ou 8 : 6 .<\/p>\n<p>2) A raz\u00e3o entre 20 e 15 \u00e9 <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-94586 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_756-Jan.-12-12.21.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"60\" height=\"58\" \/>\u00a0= ou 20 :15.<\/p>\n<p><strong>Propriedade fundamental das propor\u00e7\u00f5es<\/strong><\/p>\n<p>De um modo geral, em toda propor\u00e7\u00e3o, o produto dos extremos \u00e9 igual ao produto dos meios e vice-versa.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94588 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_757-Jan.-12-12.23.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"211\" height=\"58\" \/><\/p>\n<p>Exemplo: \u25ba Sabendo que os n\u00fameros 6, 24, 5 e x formam, nessa ordem, uma propor\u00e7\u00e3o, determine o valor de x.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94589\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_758-Jan.-12-12.25.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"104\" height=\"183\" \/><\/p>\n<p>Logo, o valor de x \u00e9 20.<\/p>\n<p>1\u00aa Propriedade: Em toda propor\u00e7\u00e3o, a soma ou a diferen\u00e7a dos dois primeiros termos est\u00e1 para o primeiro (ou para o segundo), assim com a soma ou a diferen\u00e7a dos dois \u00faltimos termos est\u00e1 para o terceiro (ou para o quarto).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94590 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_759-Jan.-12-12.26.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"387\" height=\"114\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_759-Jan.-12-12.26.jpg 387w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_759-Jan.-12-12.26-300x88.jpg 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>2\u00aa Propriedade: Em toda propor\u00e7\u00e3o, a soma (ou a diferen\u00e7a) dos antecedentes est\u00e1 para a soma (ou a diferen\u00e7a) dos consequentes, assim como cada antecedente est\u00e1 para o seu consequente.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94592 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_760-Jan.-12-12.26.jpg\" alt=\"Raz\u00f5es e Propor\u00e7\u00f5es\" width=\"293\" height=\"127\" \/><\/p>\n<p><strong>RAZ\u00d5ES:<\/strong>\u00a0Chama-se de raz\u00e3o a rela\u00e7\u00e3o entre duas grandezas, expressas na mesma unidade ou n\u00e3o. A raz\u00e3o pode ter dimens\u00e3o (ex. velocidade: m\/s, km\/h etc.) ou ser adimensional (quando dividimos coisas do mesmo tipo (\u00e1rea por \u00e1rea, etc.)<\/p>\n<p>Representa-se por: ou a: b\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 L\u00ea-se: \u201ca est\u00e1 para b\u201d<\/p>\n<p>a \u00e9 chamado antecedente.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 b \u00e9 chamado consequente.<\/p>\n<p align=\"left\"><strong>PROPOR\u00c7\u00d5ES:<\/strong>\u00a0Chama-se de propor\u00e7\u00e3o a igualdade entre duas raz\u00f5es<\/p>\n<p>Propor\u00e7\u00e3o: ou a: b = c: d\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 L\u00ea-se: \u201ca est\u00e1 para b assim como c est\u00e1 para d\u201d.<\/p>\n<p>Temos que a e d s\u00e3o os extremos enquanto que b e c s\u00e3o os meios.<\/p>\n<p><strong>RELA\u00c7\u00c3O FUNDAMENTAL DAS PROPOR\u00c7\u00d5ES:<\/strong>\u00a0\u201cEm toda propor\u00e7\u00e3o o produto dos meios \u00e9 sempre igual ao produto dos extremos.\u201d<\/p>\n<p><strong>Fonte:<\/strong>\u00a0Col\u00e9gio S\u00e3o Francisco\/centraldefavoritos.com.br\/professorwaltertadeu.mat.br<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Raz\u00e3o\u00a0\u00e9 a compara\u00e7\u00e3o matem\u00e1tica entre duas grandezas (uma divis\u00e3o), enquanto\u00a0propor\u00e7\u00e3o\u00a0\u00e9 a igualdade entre duas raz\u00f5es. Esses conceitos s\u00e3o fundamentais para resolver problemas de porcentagem, velocidade m\u00e9dia, escalas e regra de tr\u00eas. Uma\u00a0raz\u00e3o\u00a0compara duas ou mais quantidades, enquanto uma\u00a0propor\u00e7\u00e3o\u00a0\u00e9 uma equa\u00e7\u00e3o que afirma que duas raz\u00f5es s\u00e3o iguais. Juntas, elas s\u00e3o os conceitos matem\u00e1ticos fundamentais usados [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-94578","post","type-post","status-publish","format-standard","hentry","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Raz\u00f5es e Propor\u00e7\u00f5es, Grandezas, Matem\u00e1tica Raz\u00f5es e Propor\u00e7\u00f5es<\/title>\n<meta name=\"description\" content=\"Raz\u00f5es e Propor\u00e7\u00f5es, Grandezas, Matem\u00e1tica, Compara\u00e7\u00e3o, Divis\u00e3o, Raz\u00f5es, N\u00famero, Propriedade, Diferen\u00e7a, Exemplo, Raz\u00f5es e Propor\u00e7\u00f5es\" \/>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, 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